I think whether you stop your horse to allow them to poop, or make them continue to walk/trot/canter, is a matter of personal preferance and a matter of if you have a showing horse.
Personally, I let my horses stop to poop or pee. I guess I figure I wouldn't like to have to keep walking while I am trying to poop, so I figure they don't like it either. But I rarely do a showing event (like western pleasure) and when I do, it's just for fun for my barrel/rodeo horses at small local shows.
Obviously, if you show at a higher level, you can't have your horse stopping while you are in the ring or you'd be docked or disqualified for breaking gait.